Acoustoelectric amplification in resonant piezoelectric-semiconductor cavities

ABSTRACT

Interaction of acoustic waves in a piezoelectric-semiconductor resonant cavity with the charge carriers in the semiconductor layer can be directed toward amplification of the acoustic waves; such amplification scheme can be applied in building unilateral amplifiers, zero loss filters, oscillators, high detection range circuit-less wireless sensors, isolators, duplexers, circulators and other acoustic devices. An apparatus for acoustoelectric amplification is described. The apparatus includes a semiconductor layer and a thin piezoelectric layer bonded (or deposited) onto the semiconductor layer forming an acoustic cavity. Two or more tethers forming a current conduction path through the semiconductor layer and two or more access pads to silicon are positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under (Grant number ECCS 1810143) awarded by the National Science Foundation (NSF). The Government has certain rights in this invention.

BACKGROUND OF THE INVENTION

Various embodiments relate generally to acoustoelectric (AE) amplification systems, methods, devices and computer programs and, more specifically, relate to AE amplification in lateral-extensional thin-film piezoelectric-on-silicon (TPoS).

This section is intended to provide a background or context. The description may include concepts that may be pursued, but have not necessarily been previously conceived or pursued.

Unless indicated otherwise, what is described in this section is not deemed prior art to the description and claims and is not admitted to be prior art by inclusion in this section.

The acoustoelectric effect and the associated amplification has been previously utilized in surface acoustic wave (SAW) devices which has limitations in terms of operation frequency (loosing efficiency at higher frequencies), low electromechanical coupling (very low efficiency).

What is needed is a new system that overcomes such limitations.

SUMMARY

The below summary is merely representative and non-limiting.

The above problems are overcome, and other advantages may be realized, by the use of the embodiments.

In a first aspect, an embodiment provides an apparatus for acoustoelectric amplification. The apparatus includes a semiconductor layer and a thin piezoelectric layer bonded or deposited onto the semiconductor layer forming an acoustic cavity. Two or more tethers forming a current conduction path through the semiconductor layer and two or more access pads to silicon are positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer.

In another aspect, an embodiment provides a further apparatus for acoustoelectric amplification. The apparatus includes a semiconductor layer having a current isolation trench defining a suspended filter structure. A thin piezoelectric layer is bonded or deposited onto the semiconductor layer and together they form an acoustic cavity within the suspended filter structure. The apparatus also includes pairs of interdigital transducers (IDT) configured to excite and detect radio frequency signals within the suspended filter structure. Two or more access pads to silicon are positioned on two ends of the acoustic cavity and are configured to inject a DC current in the semiconductor layer within the suspended filter structure.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Aspects of the described embodiments are more evident in the following description, when read in conjunction with the attached Figures.

FIG. 1 shows a schematic of the device shows the electrode configuration for lateral field excitation (LFE) as well as points of electrical contact to Si; inset visualizes AE interaction of piezoelectric field and electrons in the device.

FIG. 2 shows theoretical and experimental insertion loss (IL) of the targeted device for different voltages (bottom)/currents (top).

FIG. 3 shows a frequency response of the device for different injected currents from 0 μA to 150 μA showing improvement in loss and quality factor (Q) as the current increases.

FIG. 4 is a scanning electron micrograph (SEM) picture of the device designed for AE amplification.

FIG. 5 shows a schematic of an embodiment having a stack cross-section and FEA simulated frequency response.

FIG. 6 shows a SEM of an A-type filter and other IDT designs.

FIG. 7 demonstrates a measured frequency response of an A-type filter before and after passing 500 μA of current.

FIG. 8 demonstrates a measured frequency response of S₂₁(S₁₂) [shown in solid(dashed)] of a D-type filter for a 0 to 400 μA current sweep, displaying the switchablity of the device.

FIG. 9 demonstrates a measured transmission/isolation response of four (4) other types of the filters.

FIG. 10 illustrates a summary of the measured AE gain and NTR of the filters as a function of current (and applied drift field) showing NTRs more than 20 dB.

FIG. 11 illustrates a schematic of an embodiment having current injected in the Si layer, AE interactions result in non-reciprocity with respect to the direction of electron flow (dashed arrow).

FIG. 12 shows a SEM of ADL200 with its corresponding electrical connections; the inset shows the close up view of the IDTs having 5 μm finger pitch.

FIG. 13 demonstrates the frequency response of ADL200 measured prior to current injection (left) while the ports are terminated to 50Ω and (right) the terminations are conjugate match of the ports of the device.

FIG. 14 shows the frequency response of ADL200 and ADL200R where the dark curves correspond to I_(DC)=0 μA and the grey ones to I_(DC)=150 μA; solid and dashed lines are respectively S₂₁ and S₁₂.

FIG. 15 shows the frequency response (|S₂₁| on the left and |S₁₂| on the right) of ADL400 terminated to 50Ω for increasing the I_(DC) from 0 to 400 μA.

FIG. 16 demonstrates the IL measured from the peak S₂₁ and S₁₂ of different ADL types measured for different values of I_(DC) showing a larger AE gain in ADL400.

FIG. 17 demonstrates the analytical curves for the acoustoelectric amplification coefficient (a) for different values of the applied drift field and free carrier concentrations for the LNoSi ADL (such as shown in FIG. 11).

FIG. 18 demonstrates the current generated by the acoustic waves propagating in the device.

DETAILED DESCRIPTION OF THE INVENTION

This patent application claims priority from U.S. Provisional Patent Application No. 62/876,268, filed Jul. 19, 2019, the disclosure of which is incorporated by reference herein in its entirety.

Utilizing the AE effect in a piezoelectric-semiconductor resonant cavity can overcome the limitations in the conventional technology, in part, by amplifying bulk acoustic waves in a structure with high electromechanical coupling that was not feasible in the past and introduce a new paradigm for transistor-less amplification at both lower and higher frequencies and non-reciprocal devices.

The AE effect is the generation of electrical signal in response to acoustic wave (or vice versa). Amplification creates a higher signal amplitude, “gain”. Resonant Cavities are structures that confine acoustic vibrations in the MHz-THz range (for RF applications) and the electrical and mechanical properties of the piezoelectric-semiconductor cavities can be tuned by independently choosing the proper materials that are employed in such devices.

Acoustic waves propagating in a piezoelectric medium are accompanied by a coupled electric field due to the piezoelectricity. In a thin piezoelectric film this field can penetrate into the surroundings and interact with charge carriers present within a certain distance. As a result, in a composite structure consisting of a thin layer of piezoelectric and semiconductor an energy exchange process exists between the propagating acoustic waves and the charge carriers in the semiconductor, from the former to the latter, leading to a loss mechanism called AE loss.

By pumping energy into the semiconductor layer through applying an electric field across it—so that the velocity of charge carriers exceed that of the acoustic wave, energy transfer can be reversed (from the charge carriers to the acoustic waves) leading to the amplification of the acoustic waves. Such phenomenon can be employed in various devices and configurations that consist of a thin stack of piezoelectric layer on a semiconductor layer such as TPoS (thin-film piezoelectric-on-Si) resonators, filters, delay lines, oscillators, etc. his is realized by placing (depositing or bonding) a layer of piezoelectric material in contact with a semiconductor substrate with proper doping concentration and forming the desired acoustic cavity and applying an electric field in parallel with the direction of acoustic wave propagation in the semiconductor layer. The described scheme can be used for building non-reciprocal amplifiers without utilizing active circuit components, near-zero insertion loss filters that eliminate the need for amplifier stages, oscillators, circuit-less quasi-passive wireless sensors with long detection range and duration of signal transmission, duplexers, isolators, and circulators. One of the more important features of the acoustoelectric amplification is that as the frequency of operation increases, the achievable gain increases too, exactly the opposite of amplification mechanism in transistor-based amplifiers where the gain-frequency product is limited.

Evidence for AE amplification in lateral-extensional TPoS resonant cavities is demonstrated. Due to the piezoelectric coupling, an evanescent electromagnetic wave is induced in the silicon (Si) layer that is a part of the resonant cavity, exchanging momentum with the carriers. Therefore, by injecting an electric current in this layer, the acoustic equivalent of Cherenkov radiation—AE amplification—can be realized. Such phenomenon is observed in a 1 GHz TPoS resonant cavity in which lateral field excitation (LFE) is utilized to excite the acoustic wave.

The acoustoelectric (AE) effect, a bi-directional coupling between the acoustic waves and electron flow (e.g., current) in a piezoelectric semiconductor (such as Cadmium Sulfide), fascinated a generation of physicists and engineers for decades during the 20^(th) century. A major implication of the AE phenomena is AE amplification of traveling bulk acoustic waves (BAW)—and later pseudo-standing due to round-trip gain in acoustic masers—using an induced DC current.

This effect has a specific criterion over relative acoustic velocity and electron drift velocity. It turns out such a condition renders the AE amplification quite inefficient in common piezoelectric semiconductors. An alternate proposal places a high mobility semiconductor substrate adjacent to a good piezoelectric substrate such that the electric field associated with the acoustic wave traveling in the piezoelectric substrate penetrates into the semiconductor. As such, structures in which a semiconductor such as silicon (Si) is held in close proximity of a Lithium Niobate (LN) substrate where surface acoustic waves (SAW) are excited and detected were proposed, yielding limited success and efficiency.

The rise of gallium nitride (GaN) as a suitable candidate for high-electron mobility and power transistors, once more, invigorated research in AE interactions, leading to demonstration of gain in BAW GaN filters, for instance. Moderate carrier concentration—improving carrier mobility and reducing the adverse effect of carrier diffusion—and high electromechanical coupling are essential for AE gain. By separating the piezoelectric and semiconductor media, these two can be chosen and adjusted independently, improving the overall amplification performance. AE gain can be realized in thin-film piezoelectric-on-silicon (TPoS) resonant devices by injecting a DC current through the Si layer. High-order lateral-extensional TPoS resonant cavities operating at 1 GHz are chosen for proving the feasibility of this concept.

A stack of 1 μm (20%) scandium doped aluminum nitride (Sc_(0.2)Al_(0.8)N)—having twice the electromechanical coupling of pure AlN (0.4% herein) while being compatible with CMOS processing—sputtered on 2 μm of lightly doped n-type Si (in the order of 1E14 cm³) forms the acoustic cavity. The electrode configuration for this resonant device is modified compared to the previous typical design as the bottom metal is removed to facilitate penetration of electric fields between the piezoelectric and the semiconductor layers (see FIG. 1). Instead, the top metal layer is redesigned to enable lateral field excitation (LFE) of the harmonic lateral-extensional resonance mode at around 1 GHz. LFE is used to ensure the electric field due to the piezoelectricity in ScAlN penetrates into the Si and exchanges momentum with the carriers within. Two extra pairs of tethers are added to the structure that form a current conduction path through the Si layer. Two access pads to silicon are also opened up on the two ends of the cavity through which a DC current is injected in the silicon. The DC contacts are isolated from the rest of the substrate to largely limit the current path through the resonant cavity.

FIG. 1 shows a schematic of the device showing the electrode configuration for LFE as well as points of electrical contact to Si; inset conceptually visualizes AE interaction of piezoelectric field and electrons in the device. The process for producing acoustoelectric amplification in lateral-extensional thin film piezoelectric-on-silicon (TPoS) resonant cavities is described below. Acoustoelectric gain is achieved by injecting a DC current through the Si layer. Potential products include: unilateral amplifiers, zero loss filters, oscillators, high detection range circuit-less wireless sensors and other acoustic wave devices (e.g., duplexers, circulators, isolators). A 0.23 dB gain has been realized with preliminary predictions showing a 50 dB gain possible.

In order to achieve an expression for the AE attenuation of composite resonant devices, the boundary condition corresponding to the set of equations for electric and elastic fields in both media are equated at their interface. This results in a dispersion equation for the system that can be modified and applied to standing wave devices as well to obtain the incremental gain due to AE effect:

$\begin{matrix} {\alpha = {K^{2}{{G\omega}\left( {\frac{\eta - 1}{\begin{matrix} {\left( {\eta - 1} \right)^{2} +} \\ {C^{2}\left( {1 + {\omega^{2}\text{/}\omega_{C}\omega_{D}}} \right)}^{2} \end{matrix}} + \frac{\eta + 1}{\begin{matrix} {\left( {\eta + 1} \right)^{2} +} \\ {C^{2}\left( {1 + {\omega^{2}\text{/}\omega_{C}\omega_{D}}} \right)}^{2} \end{matrix}}} \right)}}} & (1) \end{matrix}$

Here K is the electromechanical coupling, η is ratio of electron velocity (V_(e)) to acoustic velocity (V_(a)), ω_(c)=qμN/ε_(Si) and ω_(D)=qV_(a) ²/k_(B)Tμ are the carrier relaxation and diffusion frequency respectively, G=ε_(Si)dω_(c)[tgh(βd)/(βd]/2ε_(ScAlN)V_(a) ², and C=qμNd[tgh(βd)/(βd]/ε_(ScAlN)V_(a) where d is thickness of the Si layer, N is the free carrier concentration, β is the wave propagation constant, T is the temperature, k_(B) is Boltzmann constant, and q is elementary charge. By separating the AE attenuation coefficient from the other sources of loss (α_(total)=α_(other)+α_(AE)) the insertion loss (IL) can be written in the following form:

$\begin{matrix} {{{IL}({dB}\;)} = {20{\log_{10}\left( \frac{A_{0}e^{- \alpha}{other}^{- \alpha}{{AE}\begin{pmatrix} {{\cos \left( {{\omega t} + {\beta z}} \right)} +} \\ {\cos \left( {{\omega t} - {\beta z}} \right)} \end{pmatrix}}}{A_{0}\left( {{\cos \left( {{\omega t} + {\beta z}} \right)} + {\cos \left( {{\omega t} - {\beta z}} \right)}} \right)} \right)}}} & (2) \end{matrix}$

Hence, the term due to the AE loss can be isolated so that the right side of the equation simplifies to sum of IL at no DC current and the electric gain due to the current injection (3).

$\begin{matrix} {{20{\log_{10}\left( e^{\alpha_{AE}} \right)}} + {20{\log_{10}\left( \frac{A_{0}e^{\alpha}ot{her}^{\alpha}{{AE}\begin{pmatrix} {{\cos \left( {{\omega t} + {\beta z}} \right)} +} \\ {\cos \left( {{\omega t} - {\beta z}} \right)} \end{pmatrix}}}{A_{0}\left( {{\cos \left( {{\omega t} + {\beta z}} \right)} + {\cos \left( {{\omega t} - {\beta z}} \right)}} \right)} \right)}}} & (3) \end{matrix}$

By substituting the measured IL at no DC current in the right side term of (3) and the calculated electric gain from (1) in the left side term, the expected IL is derived and plotted in FIG. 2 for different applied voltages; the theoretical (connected by a dashed line) and experimental (connected by a solid line) IL of the targeted device for different voltages (bottom)/currents (top) are shown in FIG. 2.

While measuring the frequency response (e.g., S₂₁) of the targeted device using a Rohde & Schwarz ZNB 8 network analyzer and a pair of Cascade Microtech GSG probes at room temperature in atmospheric pressure, a DC probe is used to apply a DC voltage across the pair of Si electrical contacts and injected current is measured. The average IL of the device as a function of the applied voltage is plotted in FIG. 2 (data points are connected by solid line), showing a 0.23 dB gain by passing a ˜150 μA current which is less than the 0.48 dB expected from the theory that can be possibly due to adverse effect of joule heating in the device. The frequency response of the resonator with increasing the current is plotted in FIG. 3 and the SEM picture of the device is shown in FIG. 4.

Using AE amplification in lateral-extensional TPoS overcomes issues with the transistor-based amplifiers available today which all suffer from the limited gain-frequency product meaning that as the frequency increases, the gain decreases and reaches zero. Acoustoelectric amplification mechanism, on the other hand, becomes more efficient and offers higher gains as the frequency increases. Filtering networks introduce attenuation to the signal and require additional amplifying stages with active components while a resonant filter functioning with this scheme can be tuned to introduce no loss to the signal or amplify the signal. Sensors that offer long detection range require being accompanied by active circuits that are size and cost ineffective. The circuit-less quasi passive sensors, however, offer long detection range and transmission duration with addition of a small battery. Non-reciprocal delay-lines with zero insertion-loss can be realized using such phenomenon.

High gain unilateral amplifiers, resonant filters with zero loss, self-amplifying filters and oscillators, and long-range non-complex sensors all can be realized and are crucial for today's communication devices, especially due to the trends of internet of things, miniaturization, closely spaced narrow communication bands, and low power consumption. For instance, various embodiments can potentially replace the power-hungry amplifier stages in communication networks while consuming a power in the range of 100 μW or less.

Amplifiers and filters that incorporate the acoustoelectric amplification have the potential to substitute the conventional transistor-based amplifiers that are widely used today in many different electrical devices. The fast pace growth in the internet of things (IoT) sector requires cheap sensors with long detection ranges where the aforementioned sensors can perfectly fit in.

An embodiment provides an apparatus for acoustoelectric amplification. The apparatus includes a semiconductor layer and a thin piezoelectric layer deposited/bonded onto the semiconductor layer and forming an acoustic cavity. At least two tethers forming a current conduction path through the semiconductor layer are present. The apparatus also includes at least two access pads to silicon positioned on two ends of the acoustic cavity. These at least two access pads are configured to inject a DC current in the semiconductor layer.

In a further embodiment of the apparatus above, the thin piezoelectric layer comprises 1 μm (20%) scandium doped aluminum nitride (Sc_(0.2)Al_(0.8)N), and the semiconductor layer comprises 2 μm of lightly doped n-type Si. The materials and thicknesses used are not limited to the aforementioned ones; Aluminum nitride (which can be scandium doped), lithium niobate, gallium nitride, etc. can be used as the piezoelectric layer, having a thickness of a few nano meters to a few microns. Additionally, the semiconductor layer can be Si, Ge, compound semiconductors such as III-V materials, graphene, etc., provided that they have the proper carrier concentration and mobility.

In another embodiment of any one of the apparatus above, the at least two access pads are configured to inject the DC current so as to apply an electric field in parallel with a direction of acoustic wave propagation in the semiconductor layer.

Further embodiments enable operation as MEMS filters and delay lines with more than ˜20 dB of nonreciprocity and ˜6 dB gain. This, for instance, can potentially be implemented in the radio frequency front ends (RFFE) as the fifth generation (5G) and beyond uses full-duplex communications, that is most efficiently achieved by non-reciprocal and adaptive filters and long but miniaturized and low-loss delays.

In the 5G and beyond era in telecommunications, a great number of issues rise up that are crucial to address. Among them are the limited available frequency spectrum for data communication, interference from the transceiver module (self-interference) and from the overly congested electromagnetic spectrum (external-interference). This is because 5G relies on a great number of transceivers and antennas in the close vicinity of one another along with the additional traffic due to the internet of things (IoT) to build the communication network as a whole. As a result, full-duplexed communication along with interference mitigation architectures are inevitable as it enables doubling the communication capacity through simultaneous transmission and receive at the same frequency. Such a scheme, however, mandates integration of non-reciprocal components which are currently unavailable as the current RFFE modules are entirely implemented based on inherently reciprocal platforms. While using ferromagnetic components, material nonlinearity, or some time-varying electronic approaches have been suggested, they either suffer from miniaturization and integration issues, frequency conversion, high power consumption, or highly complex architectures (e.g., need for external clocks, switches, etc.).

Another area of interest is the tactical communications field that uses frequency selective limiters for non-reciprocal suppression of high power in-band signals that can saturate and disable the receivers, hence hindering the tactical connectivity. The possibility of miniaturized non-reciprocal components based on the AE effect may be used only a few milliwatts of power consumption which can potentially circumvent the above-mentioned issues and become a ubiquitous component in the novel communication architectures.

On the other hand, recently in the optoelectronics field, time-reversal symmetry has proven to be avoidable by employing the interaction between photons and acoustic phonons. This opens up possibilities of controlling the light propagation, achieving optical gain (laser and its bandwidth narrowing), microscopy, and material characterization. However, in order to achieve such, a high power laser is required to induce large acoustic vibrations in the structure which decreases the efficiency and practicality of this scheme. Through the AE interactions, electrons could assist in inducing larger vibrations and consequently relaxing the power requirements of the utilized laser.

A non-limiting embodiment provides a demonstration of bulk-mode lithium niobate-on-silicon (LNoSi)nonreciprocal transversal filters that exploit the acoustoelectric (AE) effect for signal amplification/attenuation. In these devices, a direct current is passed through the underlying Si layer to adjust the insertion loss (IL) and nonreciprocal transmission ratio (NTR) of the device. AE gains up to 5.6 dB with >20 dB NTR are obtainable by injecting ˜500 μA of current. This allows for merging filters, switches, and tunable attenuators in a miniaturized device which is a sought-after stepping stone for facilitating full-duplexed communications.

The AE effect, e.g., momentum exchange between electrons and acoustic phonons, ignited a great deal of research during the 20^(th) century with the goal of developing surface acoustic wave (SAW) amplifiers and signal processors. However, success was limited by the existing fabrication capabilities, discouraging researchers from further investigations. The recent demonstrations of the AE effect, from the observation of a DC current associated with acoustic waves in epitaxial AlGaN/GaN delay lines to a gain in LN/semiconductor SAW structures, is due to the advances in thin film growth and bonding techniques. Here, such effect is utilized to demonstrate bulk-mode LNoSi transversal filters with large tunable gains and nonreciprocity.

To satisfy the requirements for maximum AE coupling, e.g., high electromechanical coupling and low concentration of high-mobility electrons, an X-cut LN wafer is directly bonded to a lightly (˜7E14 cm⁻³) n-type doped (100) SOI wafer. The wafers are oriented so that the 30° off +y-axis plane of LN (that offers the highest coupling for symmetric Lamb waves) is aligned to the [110] Si plane (see FIG. 5). Twenty (20) pairs of interdigital transducers (IDT) at the two ports allow for lateral-field excitation/detection of RF signal as the bottom electrode is avoided to promote AE interactions. The IDT finger pitch (FP) determines the center of the pass-band. The lateral boundary of the suspended filter is defined by etching the device stack. This also restricts the current to pass through only the underlying Si body. The RF signal can be amplified (or attenuated) from one port to another depending on the intensity and the direction of electron drift with respect to the traveling acoustic waves, resulting in nonreciprocity and switchablity.

Table 1 summarizes the design parameters, IL, and fractional bandwidth (FBW) of the filters. The effect of device length (L), aperture (A), and electrode configuration (e.g., bidirectional or regular, split, and linearly swept FP) are studied. The SEM of an A-type filter and all the electrode configurations is displayed in FIG. 6.

TABLE 1 Types of the filters with their performance Device Type A B C D E F IDT Type Swept Reg. Reg. Reg. Reg. Split L (μm) 100 200 200 400 400 400 A (μm) 150 150 200 150 200 150 FP (μm) 5 to 6 5 5 5 5 5 IL (dB) 15.4 16.5 17.3 19.3 21.6 25.8 FBW (%) 2.8 2.1 2.3 1.6 1.9 2.7

The filters are characterized at normal temperature and pressure (NTP) by a VNA and calibrated GSG probes while a controlled current is injected through the filters with DC probes. The RF characteristic of an A-type filter before (black) and after (grey) passing a 500 μA current is shown in FIG. 7. The IL and reverse isolation are enhanced and an NTR of 4.9 dB is achieved. The same for a D-type filter for a current sweep from 0 to 400 μA is shown in FIG. 8. While the FBW is smaller than that of the A-type, a 5.6 dB gain and 19.9 dB NTR is achieved, virtually turning off the reverse transmission. The S₂₁/S₁₂ of all the other filters and the summary of the measured AE gains and NTRs are shown in FIGS. 9 and 10, respectively. The results presented high AE gain can be achieved in bulk-mode AE devices with much lower power consumption compared to the recent SAW counterparts. This suggests the possibility of developing fully-switchable near-zero IL filters through further design optimizations.

A major implication of the AE amplification in this scheme is the selective amplification that applies almost exclusively to the pass band of the device. This is in stark contrast with the transistor based amplification scheme in which signal amplification occurs non-selectively or “blindly” and is only limited by gain×bandwidth product. In other words, only the acoustic modes supported by the device that meet the AE amplification criteria are amplified. This together with proper mode isolation techniques could enable amplification schemes in which signal-to-noise ratio (SNR) is preserved or even improved. FIG. 18 shows the generation of an AE current (I_(AE)) almost exclusively within the device pass band which translates into the energy coupling between the drifting electrons and acoustic signals only at the pass band of the device. For this task, the RF port of the device is excited as the frequency is swept and the current generated by acoustic waves is recorded from the DC contacts. Generation of this AE current almost exclusively within the device pass band enables frequency selective amplification.

Another embodiment provides lithium niobate-on-silicon (LNoSi) non-reciprocal acoustic delay lines (ADL) with tunable insertion loss (IL) utilizing the acoustoelectric (AE) effect Due to the AE effect, the direction- and the intensity-dependent momentum exchange between the drifting electrons in the Si layer and the acoustic phonons can be utilized to break the intrinsic reciprocity of the ADLs in order to control their frequency response. A 5.2 dB improvement in the IL and a 14.2 dB increase in the reverse isolation (e.g., a 19.4 dB non-reciprocal transmission ratio) is achieved through injecting a 400 μA current in one of the ADLs presented here. This opens up possibilities of merging long delays, tunable attenuators, and switches in a single miniaturized device which is a critical stepping stone in fulfillment of full-duplexed microwave systems.

While the revolution in electronics mainly relied on silicon (Si) and it continues to be driven by it, lithium niobate (LN) is playing the same role in the integrated photonics field. As a result, hybrid electro-optic devices will likely be realized on LN on Si (LNoSi) heterogeneous platforms. Furthermore, due to its outstanding piezoelectric properties, LN has been long studied and employed in radio frequency (RF) acoustics for signal processing applications. More specifically, a great deal of research on the acoustoelectric (AE) phenomenon was fueled once LN-semiconductor heterostructures were preceded by piezoelectric semiconductor materials as the testbed for studying such phenomenon in the 1960s. The AE effect was initially observed in the form of the attenuation of acoustic phonons in an electron plasma as a result of the momentum transfer from former to latter, eventually, it was employed in surface acoustic wave (SAW) AE amplifiers by drifting electrons faster than the phase velocity of the acoustic waves (AW) in a manner similar to a travelling-wave-tube amplifier. However, limited fabrication capabilities at the time and subsequently devices with low efficiency discouraged many researchers from further investigations.

It was until recently that advances in wafer-level bonding enabled new demonstrations of the AE effect in heterogeneous SAW structures based on LN while our group demonstrated such effect in thin-film piezoelectric-on-Si (TPoS) Lamb wave resonators. The AE interactions in the latter comprises the piezoelectric coupling as well as the deformation potential, both of which contribute to the anharmonic electron bunching due to the stress in the piezoelectric film and Si layer, respectively. Utilizing such interactions in LNoSi platform enable realization of non-reciprocal Lamb wave acoustic delay lines (ADL) that concurrently allow for tuning the insertion loss (IL) and switching. In this scheme, the inherent reciprocity of such components is broken by the drifting electrons in the underlying Si layer; as it amplifies the signals (e.g., AW) propagating in its direction while attenuating those that propagate in the opposite direction. Such capabilities in a single miniaturized component facilitate the implementation of full-duplexed communications and mitigation of interference in the congested RF spectrum, both of which are essential to the 5G and beyond networks.

FIG. 11 illustrates a schematic of an embodiment having current injected in the Si layer, AE interactions result in non-reciprocity with respect to the direction of electron flow (dashed arrow).

In order to maximize the AE interactions, a high electromechanical coupling in conjunction with a low concentration of high mobility electrons is desired. To satisfy such conditions, an X-cut LN wafer is directly bonded to a lightly n-type doped 4-inch (100) SOI wafer. The wafers are oriented so that the 30° off +y-axis plane of LN that is commonly known to offer the highest coupling for the symmetric Lamb waves is aligned to the [110] plane of the Si which allows for the highest electron mobility. The device structure is schematically displayed in FIG. 11. The device stack consists of 1 μm LN and 3 μm Si at a doping level of ˜7E14 cm³.

Lamb waves are launched by means of 20 pairs of interdigital transducers (IDT) made of a 100 nm thick molybdenum (Mo) layer from one port and detected at the second port after propagating through the delay region. By utilizing the lateral field excitation, the device structure may omit a bottom electrode. This allows for the strong penetration of the piezoelectrically coupled electric fields into the Si layer and guarantees stronger AE interactions.

The IDT finger pitch, defined as the centertocenter distance between two consecutive electrodes, determines the center of the ADL pass-band and is chosen to be 5 μm in this non-limiting embodiment. The freedom in the IDT pattern which spatially maps the frequency pass band of the ADL can be used to accommodate a variety of pass band responses (e.g., narrow-band, wide-band). The length of the delay region determines the insertion delay (ID) as well as the amount of AE gain and non-reciprocity. Delay lengths of 200 μm (ADL200) and 400 μm (ADL400) are demonstrated below which respectively correspond to 30 ns and 60 ns real-time ID. Longer delay lengths correspond to longer real time delay, for instance a real time delay of ˜0.6 ns can be expected in a ADL having 4 mm of delay length.

The lateral boundary of the device is defined by etching the device stack which also restricts the current to pass only through the ADL. In-plane acoustic reflectors are incorporated in one of the configurations (ADL200R) to illustrate its effect. In order to pass current through the underlying Si, contacts are formed by etching the LN film and depositing gold (Au) and the ADL is suspended by etching the backside handle layer. The scanning electron micrograph (SEM) of a fabricated device and its IDT is shown in FIG. 12, a SEM of ADL200 with its corresponding electrical connections; the inset shows the close up view of the IDTs having 5 μm finger pitch.

The current values passing through the device are demonstrated since they directly impact the AE interactions. By doing so, the parasitic effects of non-Ohmic junctions between Au and lightly n-Si is mostly avoided.

Depending on the current intensity and direction, the propagating AWs can be attenuated or amplified along the ADL from one port to another with the AE gain (G_(AE)) expression being

G _(AE) =e ^(αL)  (4)

where α is the incremental gain coefficient, and L is the device length. The incremental gain is generally expressed in the form of

$\begin{matrix} {{\alpha \text{/}k_{0}} = {\frac{K^{2}}{2}\frac{\gamma \omega \tau}{1 + \left( {\gamma \omega \tau} \right)^{2}}}} & (5) \end{matrix}$

where k₀ and ω are the wavenumber and angular frequency, K² is the electromechanical coupling, y is the relative difference between the electron drift velocity and AW phase velocity, and τ is a time constant that is determined by the conductivity and permittivity of the structure. It can be inferred from Eq. (4) that the longer the ADL, the more AE gain and subsequently loss compensation is achievable. This directly translates to longer ID with lower IL; as the AE gain overcompensates for the propagation loss which has been reported to be ˜1 dB·mm⁻¹ in such class of LN ADLs while Si is a very low acoustic loss material, as well.

FIG. 17 demonstrates the analytical curves for the acoustoelectric amplification coefficient (a) for different values of the applied drift field and free carrier concentrations for the LNoSi ADL (such as shown in FIG. 11).

The devices are characterized at normal temperature and pressure by a vector network analyzer using ground signal ground (GSG) microprobes after performing on chip short-open-load-thru calibration to move the reference plane to the microprobe tips. Meanwhile, a pair of DC probes are used to feed the ADL with a voltage source with a controlled current (I_(DC)). FIG. 13 shows the measured frequency response (magnitude of the S-parameters) of ADL200 terminated to 50Ω (left) and a conjugately matched load (right) prior to passing I_(DC). The ADL shows reciprocity and the fractional bandwidth (FBW) is measured to be 2.1% while the IL is 19.2 dB and 16.5 dB before and after performing the single stage low pass LC matching using the Keysight ADS software, respectively.

FIG. 14 shows the frequency response of ADL200 and ADL200R where the dark curves correspond to I_(DC)=0 μA and the grey ones to I_(DC)=150 μA; solid and dashed lines are respectively S₂₁ and S₁₂.

Next, I_(DC) is passed through the ADLs while their RF characteristics is measured. The IL is improved once the electron drift is in the same direction as the propagating RF signal while the reverse isolation is also enhanced due to the AE attenuation of backscattering waves. FIG. 14 compares the magnitude of S₂₁ and S₁₂ of the ADL200 and ADL200R before and after passing I_(DC)=150 μA through them. While the S₂₁ and S₁₂ overlap without passing the current, such amount of current results in a non-reciprocal transmission ratio (NTR=|S₂₁|/|S₁₂|) of 5.3 dB and 2.7 dB, respectively. Terminating the ADL with the acoustic reflector improves the IL at the expense of reducing the attainable NTR.

FIG. 15 shows the frequency response (|S₂₁| on the left and |S₁₂| on the right) of ADL400 terminated to 50Ω for increasing the Inc from 0 to 400 μA. The transmission and reverse isolation of ADL400 are shown as the injected current is increased. The IL and NTR of the ADL is tunable by changing the I_(DC), yielding a 5.2 dB enhancement in the IL with a 19.4 dB of NTR at I_(DC)=400 μA. Additionally, with reversing the current flow, the direction of the changes in the S₂₁ and S₁₂ is reversed and the ADL is virtually switched off at such current. The measured peak S₂₁ and S₁₂ of the devices studied herein for a current sweep from 0 to 250 μA is plotted in FIG. 16, confirming that a larger AE gain and NTR is achievable in the longer ADL.

An additional knob for fine-tuning the AE gain is available by applying a bias to the top IDTs and take advantage of the metal-insulator-semiconductor capacitor that is inherently formed in the disclosed structures. By applying the bias to the IDTs, the semiconductor layer (Si herein) can be depleted from charge carriers or accumulated. Such carrier density variations allow for adjusting the AE gain and non-reciprocity independent from the main bias voltage that is used for carrier drift. This additionally allows for compensating the variations of the carrier concentration from the values targeted in the design as a result of perturbations for example during the wafer bonding or etc.

By using the momentum exchange between the acoustic phonons and electrons, e.g., acoustoelectric effect (AE), in lithium niobate on silicon heterostructures, various embodiments can enable non-reciprocal Lamb wave acoustic delay lines (ADL) that can provide long delays with switching capabilities in a single miniaturized device. By passing a direct current through the lightly doped Si layer, the insertion loss (IL), reverse isolation, and non-reciprocal transmission ratio (NTR) of the ADLs can be manipulated and at a constant current, a higher tuning range for the IL and NTR is achievable for longer devices.

The foregoing description has been directed to particular embodiments. However, other variations and modifications may be made to the described embodiments, with the attainment of some or all of their advantages. Modifications to the above-described systems and methods may be made without departing from the concepts disclosed herein. Accordingly, the invention should not be viewed as limited by the disclosed embodiments. Furthermore, various features of the described embodiments may be used without the corresponding use of other features. Thus, this description should be read as merely illustrative of various principles, and not in limitation of the invention. 

What is claimed is:
 1. An apparatus for acoustoelectric amplification, the apparatus comprising: a semiconductor layer; a thin piezoelectric layer bonded onto the semiconductor layer and forming an acoustic cavity; at least two tethers forming a current conduction path through the semiconductor layer; and at least two access pads to silicon positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer.
 2. The apparatus of claim 1, wherein the thin piezoelectric layer comprises 1 μm (20%) scandium doped aluminum nitride (Sc_(0.2)Al_(0.8)N), and the semiconductor layer comprises 2 μm of lightly doped n-type Si.
 3. The apparatus of claim 1, wherein the at least two access pads are configured to inject the DC current so as to apply an electric field in parallel with a direction of acoustic wave propagation in the semiconductor layer.
 4. An apparatus for acoustoelectric amplification, the apparatus comprising: a semiconductor layer; a thin piezoelectric layer deposited onto the semiconductor layer and forming an acoustic cavity; at least two tethers forming a current conduction path through the semiconductor layer; and at least two access pads to silicon positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer.
 5. The apparatus of claim 4, wherein the thin piezoelectric layer comprises 1 μm (20%) scandium doped aluminum nitride (Sc_(0.2)Al_(0.8)N), and the semiconductor layer comprises 2 μm of lightly doped n-type Si.
 6. The apparatus of claim 4, wherein the at least two access pads are configured to inject the DC current so as to apply an electric field in parallel with a direction of acoustic wave propagation in the semiconductor layer.
 7. An apparatus for acoustoelectric amplification, the apparatus comprising: a semiconductor layer having a current isolation trench defining a suspended filter structure; a thin piezoelectric layer bonded onto the semiconductor layer and forming an acoustic cavity within the suspended filter structure; a plurality of pairs of interdigital transducers (IDT) configured to excite and detect radio frequency signals within the suspended filter structure; and at least two access pads to silicon positioned on two ends of the acoustic cavity and configured to inject a DC current in the semiconductor layer within the suspended filter structure.
 8. The apparatus of claim 7, wherein the plurality of pairs of IDTs comprise at least twenty pairs of IDTs.
 9. The apparatus of claim 7, wherein the semiconductor layer defines at least one acoustic delay line (ADL) within the suspended filter structure.
 10. The apparatus of claim 9, wherein the at least two access pads are configured to inject the DC current into the at least one ADL.
 11. The apparatus of claim 7, wherein the semiconductor layer is a lightly n-type doped (100) SOI wafer.
 12. The apparatus of claim 7, wherein the plurality of pairs of IDTs comprise a molybdenum (Mo) layer.
 13. The apparatus of claim 12, wherein the molybdenum (Mo) layer is approx. 100 nm thick.
 14. The apparatus of claim 7, wherein the plurality of pairs of IDTs comprise a molybdenum (Mo) layer.
 15. The apparatus of claim 7, wherein the plurality of pairs of IDTs have a finger pitch of 5 μm.
 16. The apparatus of claim 7, wherein the plurality of pairs of IDTs are separated by a delay region.
 17. The apparatus of claim 16, wherein the delay region is between 200 μm and 400 μm.
 18. The apparatus of claim 7, wherein the apparatus is configured to receive separate biases to the plurality of pairs of IDTs in order to modify carrier concentration in the semiconductor layer enabling fine-tuning of acoustoelectric amplification and nonreciprocity 